$10\mathrm{.}10$ The load impedance in Fig. P$10\mathrm{.}10$ absorbs $40$ kW and $30$ kVAR $.$ The sinusoidal voltage source develops $50$ kW $.$

a$.$ Find the values of capacitive line reactance that will satisfy these constraints.

b$.$ For each value of line reactance found in $($a$),$ show that the magnetizing vars developed equals the magnetizing vars absorbed$.$

Figure P$10\mathrm{.}10$